text: For two N particle systems 0 and 1 with partition function  and  ,  
  from 
  get the thermodynamic free energy difference is 
  For every configuration visited during this sampling of system 1 we can compute the potential energy U as a function of the configuration space, and the potential energy difference is 
  Now construct a probability density of the potential energy from the above equation:
  where in  is a configurational part of a partition function
  since 
  now define two functions:
  thus that 
  and can be obtained by fitting  and